### Abstract

We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and scattering matrices. If the particles are bound states then the leading exponential finite-size corrections (μ-terms) are related to virtual processes in which the particles disintegrate into their constituents. For non-bound state particles the leading exponential finite-size corrections (F-terms) come from virtual particles traveling around the finite world. In these F-terms a specifically regulated infinite volume form factor is integrated for the momenta of the virtual particles. The F-term is also present for bound states and the μ-term can be obtained by taking an appropriate residue of the F-term integral. We check our results numerically in the Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian truncations.

Original language | English |
---|---|

Article number | 173 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1 2019 |

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### Keywords

- Field Theories in Lower Dimensions
- Integrable Field Theories
- Nonperturbative Effects

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2019*(7), [173]. https://doi.org/10.1007/JHEP07(2019)173

**Leading exponential finite size corrections for non-diagonal form factors.** / Bajnok, Z.; Lájer, Márton; Szépfalvi, Bálint; Vona, István.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2019, no. 7, 173. https://doi.org/10.1007/JHEP07(2019)173

}

TY - JOUR

T1 - Leading exponential finite size corrections for non-diagonal form factors

AU - Bajnok, Z.

AU - Lájer, Márton

AU - Szépfalvi, Bálint

AU - Vona, István

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and scattering matrices. If the particles are bound states then the leading exponential finite-size corrections (μ-terms) are related to virtual processes in which the particles disintegrate into their constituents. For non-bound state particles the leading exponential finite-size corrections (F-terms) come from virtual particles traveling around the finite world. In these F-terms a specifically regulated infinite volume form factor is integrated for the momenta of the virtual particles. The F-term is also present for bound states and the μ-term can be obtained by taking an appropriate residue of the F-term integral. We check our results numerically in the Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian truncations.

AB - We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and scattering matrices. If the particles are bound states then the leading exponential finite-size corrections (μ-terms) are related to virtual processes in which the particles disintegrate into their constituents. For non-bound state particles the leading exponential finite-size corrections (F-terms) come from virtual particles traveling around the finite world. In these F-terms a specifically regulated infinite volume form factor is integrated for the momenta of the virtual particles. The F-term is also present for bound states and the μ-term can be obtained by taking an appropriate residue of the F-term integral. We check our results numerically in the Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian truncations.

KW - Field Theories in Lower Dimensions

KW - Integrable Field Theories

KW - Nonperturbative Effects

UR - http://www.scopus.com/inward/record.url?scp=85069895557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069895557&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2019)173

DO - 10.1007/JHEP07(2019)173

M3 - Article

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 173

ER -